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Novel topological insulators from crystalline symmetries

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  • Published: 21 November 2018
  • volume 227, pages 1309–1321 (2018)
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Novel topological insulators from crystalline symmetries
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  • Alexander Lau1 &
  • Carmine Ortix2,3 
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Abstract

We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions (3D), these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the appearance of these topological states in both crystals with negligible spin–orbit coupling and a fourfold rotational symmetry, as well as in mirror-symmetric crystals with sizable spin–orbit interaction characterized by the so-called mirror Chern number. Finally, we also discuss similar topological crystalline states in one-dimensional (1D) insulators, such as nanowires or atomic chains, with mirror symmetry. There, the prime physical consequence of the non-trivial topology is the presence of quantized end charges.

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Author information

Authors and Affiliations

  1. Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 4056, 2600 GA, Delft, The Netherlands

    Alexander Lau

  2. Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    Carmine Ortix

  3. Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, 84084, Fisciano, Italy

    Carmine Ortix

Authors
  1. Alexander Lau
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  2. Carmine Ortix
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Correspondence to Alexander Lau.

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Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cite this article

Lau, A., Ortix, C. Novel topological insulators from crystalline symmetries. Eur. Phys. J. Spec. Top. 227, 1309–1321 (2018). https://doi.org/10.1140/epjst/e2018-800098-y

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  • Received: 31 May 2018

  • Revised: 29 August 2018

  • Published: 21 November 2018

  • Issue Date: December 2018

  • DOI: https://doi.org/10.1140/epjst/e2018-800098-y

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Topological States of Matter: Theory and Applications

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